Date post: | 06-May-2015 |
Category: |
Education |
Upload: | collaborative-for-teaching-and-learning |
View: | 635 times |
Download: | 1 times |
Mathematics Summit
Southern Indiana Deanery: Focus on Mathematics Instruction
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Standards for the Day
• Deepen understanding of new Common Core State Standards for mathematics
• Create understanding of using multiple representations and approaches to problem solving
• Apply a variety of strategies to support and promote the learning of mathematics
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Agenda
DAY II• Analysis of New Common Core State Standards• Using Multiple Representations to Develop Deeper
Understanding • Using Number lines and manipulatives to support
conceptual understanding
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Quick Write
From our time together yesterday,
What ideas, strategies, concepts, routines do you want to revisit as you plan your classroom for the upcoming year? Which do you want to focus on initially? & How do you plan on accomplishing this?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Reasoning Abstractly and Quantitatively
• 5.NBT.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
• Working in non-grade level groups (2-3)
Divide 365÷4 (by hand) using three different methods.
(Keep in mind, we are developing reasoning and sense-making, and multiple approaches/methods
to use with our students )
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Method 1 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Method 2 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Method 3 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Method 4 of ∞
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Method 5 of ∞
112/4 = 28
112/4 = 28
112/4 = 28
24/4 = 6 5/4 = 1 R1
365 = 112+112+112+24+5 = 28+28+28+6+1+¼ = 91¼ 4 4
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Common Core State Standards for MathematicsK-8 Mathematics Content
DOMAINS Counting & Cardinality
Operations & Algebraic Thinking
Number & Operations in Base
Ten
Measurement & Data Geometry
Number & Operations:
Fractions
Ratios & Proportional Relationships
The Number System
Expressions & Equations
Statistics & Probability Functions
K X X X X X
1 X X X X
2 X X X X
3 X X X X X
4 X X X X X
5 X X X X X
6 X X X X X
7 X X X X X
8 X X X X X
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
6 7 8
Proportional Relationships
Understand ratio concepts and use ratio reasoning to solve problems
Analyze proportional relationships and use them to solve real world and mathematical ‐problems.
The Number System
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Compute fluently with multi digit numbers ‐and find common factors and multiples.
Apply and extend previous understandings of numbers to the system of rational numbers.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations
Apply and extend previous understandings of arithmetic to algebraic expressions.
Reason about and solve one variable ‐equations and inequalities.
Represent and analyze quantitative relationships between dependent and independent variables.
Use properties of operations to generate equivalent expressions.
Solve real life and mathematical problems ‐using numerical and algebraic expressions and equations.
Work with radicals and integer exponents. Understand the connections between
proportional relationships, lines, and linear equations.
Functions Define, evaluate, and compare functions. Use functions to model relationships
between quantities.
Geometry Solve real world and mathematical ‐problems involving area, surface area, and volume.
Draw, construct and describe geometrical figures and describe the relationships between them.
Solve real life and mathematical problems ‐involving angle measure, area, surface area, and volume.
Understand congruence and similarity using physical models, transparencies, or geometry software.
Understand and apply the Pythagorean Theorem.
Solve real world and mathematical ‐problems involving volume of cylinders, cones, and spheres.
Statistics and Probability
Develop understanding of statistical variability.
Summarize and describe distributions.
Use random sampling to draw inferences about a population.
Draw informal comparative inferences about two populations.
Investigate chance processes and develop, use and evaluate probability models.
Investigate patterns of association in bivariate data.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Content Analysis
In grade level groups:
• Identify new content for your grade level
• Identify different opportunities for using multiple representations, approaches, number forms
• Develop a priority list of content & approaches to be developed during the transition period.
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Content Analysis
In school groups:
• Outline content priorities at each grade level
• Identify both major and minor shifts
• Shift emphases – decide that teachers will pay more attention to x and y in 2011-2012 and less attention to z
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Quick Write
Based on this morning’s conversations, what do you want to remember? How have you added any more thinking to the routines/processes that you are planning on implementing this year?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Working with Manipulatives
• Don’t assume that students make the connections between the different forms/representations of the problems
• As with any process, students need to develop understanding of the process prior to attempting to learn new material.
You must be intentional in doing this!
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
How do we represent in mathematics?
Number
Algebra
Graphical
Sentence
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
CTL, Mathematical Literacy
21
Grade Level Content
Working in multi-grade groups work throughseveral of the problems on the page.
What does it look like?How do the ideas progress across the grades?How do I support, develop student skills in this area?
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Literacy in Mathematics
Vocabulary Development
Reading
Writing2Speaking/ Listening
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Community Wiki
sidmath.pbworks.com
Collaborative for Teaching and Learning SID: Focus on Mathematics Instruction
August 3, 2011
Community Wiki
sidmath.pbworks.com
By the way, what is a Wiki?